How to model inhibitory synapses in the artificial neuron?
Principles of Computational Modelling in Neuroscience by David Sterratt, Bruce Graham, Andrew Gillies and David Willshaw discuss it in Chapter 7 (The synapse) and also in Chapter 8 (Simplified models of neurons). Especially in chapter 8, they discuss how to add excitatory or inhibitory synapses to integrate and fire neuron. 

There are various ways to add inhibitory synapse: either substrate voltage, inject negative current.